Question: Simplify the following expression: $\dfrac{4y^2}{44y^2}$ You can assume $y \neq 0$.
$ \dfrac{4y^2}{44y^2} = \dfrac{4}{44} \cdot \dfrac{y^2}{y^2} $ To simplify $\frac{4}{44}$ , find the greatest common factor (GCD) of $4$ and $44$ $4 = 2 \cdot 2$ $44 = 2 \cdot 2 \cdot 11$ $ \mbox{GCD}(4, 44) = 2 \cdot 2 = 4 $ $ \dfrac{4}{44} \cdot \dfrac{y^2}{y^2} = \dfrac{4 \cdot 1}{4 \cdot 11} \cdot \dfrac{y^2}{y^2} $ $\phantom{ \dfrac{4}{44} \cdot \dfrac{2}{2}} = \dfrac{1}{11} \cdot \dfrac{y^2}{y^2} $ $ \dfrac{y^2}{y^2} = \dfrac{y \cdot y}{y \cdot y} = 1 $ $ \dfrac{1}{11} \cdot 1 = \dfrac{1}{11} $